Modified minimum principal stress estimation formula based on Hoek–Brown criterion and equivalent Mohr–Coulomb strength parameters

The most critical parameter for determining equivalent values for the Mohr–Coulomb friction angle and cohesion from the nonlinear Hoek–Brown criterion is the upper limit of confining stress. For rock slopes, this value is the maximum value of the minimum principal stress ( $$\sigma_{3,\max }^{\prime }$$σ 3 , max ′ ) on the potential failure surface. The existing problems in the existing research are analyzed and summarized. Using the finite element method (FEM), the location of potential failure surfaces for a wide range of slope geometries and rock mass properties are calculated using the strength reduction method, and a corresponding finite element elastic stress analysis was carried in order to determine $$\sigma_{3,\max }^{\prime }$$σ 3 , max ′ of the failure surface. Through a systematic analysis of 425 different slopes, it is found that slope angle (β) and geological strength index (GSI) have the most significant influence on $$\sigma_{3,\max }^{\prime }$$σ 3 , max ′ while the influence of intact rock strength and the material constant $$m_{i}$$m i are relatively small. According to the variation of $$\sigma_{3,\max }^{\prime }$$σ 3 , max ′ with different factors, two new formulas for estimating $$\sigma_{3,\max }^{\prime }$$σ 3 , max ′ are proposed. Finally, the proposed two equations were applied to 31 real case studies to illustrate the applicability and validity.